When LLM agents give conflicting answers, voting and LLM judges aggregate only forward predictions, so shared errors can persist. The authors instead construct a reverse posterior for each instance via Bayesian backward reasoning from an explicit likelihood, giving a differently factorized approximation of the class posterior. They rank agents by Jensen-Shannon divergence between each forward posterior and this reverse anchor, yielding three strategies: hard selection (MinJS), soft reweighting (FwdJS), and log-linear fusion (LogLin).
On DDXPlus across five LLM backbones, MinJS beat random selection, FwdJS generally improved over the strongest baseline, and LogLin performed best, especially where agents disagreed. The reverse posterior's standalone accuracy was weaker, but it worked better as an anchor than forward-only alternatives. A lightweight two-stage calibration further improved aggregation when labeled data were available.